Find the derivative of f(x).

1. f(x)=(2x^3－4x^2+3)/x^2
Sol
y=(2x^3－4x^2+3)/x^2
yx^2=2x^3－4x^2+3
2xy+x^2y'=6x^2－8x
x^2y'=6x^2－8x－2xy
x^2y'=6x^2－8x－2x(2x^3－4x^2+3)/x^2
x^3y'=6x^3－8x^2－2(2x^3－4x^2+3)
x^3y'=2x^3－6
y'=(2x^3－6)/x^3

2. f(x)=(4x^3－3x^2+2x+5)/x^2
Sol
y=(4x^3－3x^2+2x+5)/x^2
yx^2=4x^3－3x^2+2x+5
2xy+x^2y'=12x^2－6x+2
x^2y'=12x^2－6x+2－2xy
x^2y'=12x^2－6x+2－2x(4x^3－3x^2+2x+5)/x^2
x^3y'=12x^3－6x^2+2x－2(4x^3－3x^2+2x+5)
x^3y'=4x^3－2x－10
y'=(4x^3－2x－10)/x^3

圖片參考：http://i256.photobucket.com/albums/hh172/hkchelsea_united/20101107_1.png


圖片參考：http://i256.photobucket.com/albums/hh172/hkchelsea_united/20101107_2.png



If you have any questions, please feel free to ask.

2010-11-14 03:22:31 補充：
題目本來無 y, 又沒有將 y 定義. 更無緣無故來個 implicit differentiation... 不明白為何 002 會這樣做...